In a mixing bowl, combine 1 cup of flour, ⅓ cup of icing sugar, ¼ cup of cocoa powder, and ¼ teaspoon of salt. Pour in melted butter and vanilla extract, stirring until a dough forms. Press the mixture evenly into a tart pan and chill in the refrigerator for at least 30 minutes.

Whisk together egg yolks, whole eggs, white sugar, cornstarch, and salt in a bowl until smooth and creamy. Heat whole milk and heavy cream in a saucepan until just simmering, then gradually whisk it into the egg mixture.

Melt dark chocolate until smooth and gradually whisk it into the custard mixture until fully integrated.

Pour the chocolate custard into the pre-baked tart shell. Place the tart pan in a larger baking dish and add hot water, creating a water bath. Bake in a preheated oven at 350°F for about 40-50 minutes.

Remove from the water bath and cool to room temperature, then refrigerate for several hours or overnight. Brush the surface with jam before serving.